I think what was asked was “what, if anything, made a ‘Lord’ Inelligible to sit in the House of Commons?” In short, the moment you are a member of the UK House of Lords, you may not sit in the House of Commons. Prior to 1999, if you ‘came into’ your peerage (in other words, were a Lord outright and not merely entitled to the ‘courtesy’ title - as say the son of an Earl was entitled to the courtesy title of ‘Viscount’ before he came into his father’s title upon his death) you immediately became ineligible to be elected to or to sit in the House of Commons. For the Americans, it is somewhat comparable to being prohibited from sitting in both the House if Representatives and the Senate, or perhaps one of the chambers of Congress and the Executive offices.
After the 1999 Act, one was not immediately eligible to sit in the House of Lords upon ‘coming into’ a title as had been the case prior to the Act’s adoption (prior to this the means of ‘wagering’ votes in the Lords was for the Monarch to appoint Life Peers as a means to dilute the numbers of the Hereditary Peers), and as it stands now the only way to become ineligible is to be elected by the Hereditary Peers to sit in the Lords AND to accept such election, to be granted a Life Peerage senior to a Hereditary Peerage already held, or to be given a Life Peerage and to accept it as a commoner. In any event, the moment you sit in the Lords you may NOT sit in the Commons.
How’s that for an American Academic?